Context. In view of the recent problem regarding the dynamical modelling of winds of M-type AGB stars (insufficient radiation pressure on silicate grains), some of the basic assumptions of these ...models need to be re-evaluated critically. Aims. Accepting the conclusion that non-grey effects will force silicate grains to be virtually Fe-free, the viability of driving winds with micron-sized Fe-free silicates, instead of small particles, is examined. Methods. Using both simple estimates and detailed dynamical atmosphere and wind models, it is demonstrated that radiation pressure on Fe-free silicate grains is sufficient to drive outflows if the restriction to the small particle limit is relaxed, and prevailing thermodynamic conditions allow grains to grow to sizes in the micrometer range. Results. The predicted wind properties, such as mass loss rates and outflow velocities, are in good agreement with observations of M-type AGB stars. Due to a self-regulating feedback between dust condensation and wind acceleration, grain growth naturally comes to a halt at particle diameters of about $1~\mu$m. Conclusions. The most efficient grain sizes to drive winds are in a rather narrow interval around $1~\mu$m. These values are set by the wavelength range corresponding to the flux maximum in typical AGB stars, and are very similar to interstellar grains.
Context. In recent years, high spatial resolution techniques have given valuable insights into the complex atmospheres of AGB stars and their wind-forming regions. They make it possible to trace the ...dynamics of molecular layers and shock waves, to estimate dust condensation distances, and to obtain information on the chemical composition and size of dust grains close to the star. These are essential constraints for understanding the mass loss mechanism, which presumably involves a combination of atmospheric levitation by pulsation-induced shock waves and radiation pressure on dust, forming in the cool upper layers of the atmospheres. Aims. Spectro-interferometric observations indicate that Al2O3 condenses at distances of about 2 stellar radii or less, prior to the formation of silicates. Al2O3 grains are therefore prime candidates for producing the scattered light observed in the close vicinity of several M-type AGB stars, and they may be seed particles for the condensation of silicates at lower temperatures. The purpose of this paper is to study the necessary conditions for the formation of Al2O3 and the potential effects on mass loss, using detailed atmosphere and wind models. Methods. We have constructed a new generation of Dynamic Atmosphere and Radiation-driven Wind models based on Implicit Numerics (DARWIN), including a time-dependent treatment of grain growth and evaporation for both Al2O3 and Fe-free silicates (Mg2SiO4). The equations describing these dust species are solved in the framework of a frequency-dependent radiation-hydrodynamical model for the atmosphere and wind structure, taking pulsation-induced shock waves and periodic luminosity variations into account. Results. Condensation of Al2O3 at the close distances and in the high concentrations implied by observations requires high transparency of the grains in the visual and near-IR region to avoid destruction by radiative heating. We derive an upper limit for the imaginary part of the refractive index k around 10-3 at these wavelengths. For solar abundances, radiation pressure due to Al2O3 is too low to drive a wind. Nevertheless, this dust species may have indirect effects on mass loss. The formation of composite grains with an Al2O3 core and a silicate mantle can give grain growth a head start, increasing both mass loss rates and wind velocities. Furthermore, our experimental core-mantle grain models lead to variations of visual and near-IR colors during a pulsation cycle which are in excellent agreement with observations. Conclusions. Al2O3 grains are promising candidates for explaining the presence of gravitationally bound dust shells close to M-type AGB stars, as implied by both scattered light observations and mid-IR spectro-interferometry. The required level of transparency at near-IR wavelengths is compatible with impurities due to a few percent of transition metals (e.g., Cr), consistent with cosmic abundances. Grains consisting of an Al2O3 core and an Fe-free silicate mantle with total grain radii of about 0.1−1 micron may be more efficient at driving winds by the scattering of stellar photons than pure Fe-free silicate grains.
Context. Winds of asymptotic giant branch stars are assumed to be driven by radiation pressure on dust. Previously, this process has been modeled with detailed time-dependent simulations of ...atmospheres and winds assuming spherically symmetric flows. In such models kinetic energy is injected by a variable inner boundary (“piston”) simulating the effects of stellar pulsation. However, the dynamical processes in these atmospheres – convection and pulsations – are actually three-dimensional. Aims. We present and analyze first 3D radiation hydrodynamics simulations of the convective interior and the atmosphere of a typical AGB star. In particular, we check whether the piston description in the 1D wind models is compatible with the 3D results. Methods. We used two different RHD codes, one (CO5BOLD) to produce 3D models of the outer convective envelope and the inner atmosphere of an AGB star, the other to describe the atmosphere and the wind acceleration region, including dust formation and non-grey radiative transfer, but assuming spherically symmetric flows. From the movements of stellar surface layers in the 3D models, we derived a description for the variable inner boundary in the 1D models. Results. The 3D models show large convection cells and pulsations that give rise to roughly spherically expanding shock waves in the atmosphere, levitating material into regions which are cool enough to allow for dust formation. The atmospheric velocity fields have amplitudes and time scales close to the values that are necessary to start dust formation in the 1D wind models. Conclusions. The convection cells in the 3D simulations are so large that the associated shock fronts appear almost spherical, justifying the assumption of spherical symmetry and the use of a piston boundary condition in the context of wind models. Nevertheless, certain non-radial structures exist in the dust shell developing in the 3D simulations which should be detectable with current interferometric techniques.
Context.
The characteristic variability of cool giants and supergiants is attributed to a combination of stellar pulsation and large-scale convective flows. Full 3D radiation-hydrodynamical modelling ...is an essential tool for understanding the nature of these dynamical processes. The parameter space in our 3D model grid of red giants has expanded in recent years. These models can provide many insights on the nature and properties of the pulsations, including the interplay between convection and pulsations.
Aims.
We treat 3D dynamical models of asymptotic giant branch (AGB) stars and red supergiants (with current masses 1
M
⊙
≤
M
*
≤ 12
M
⊙
) similar to observational data. We aim to explore the relation between stellar parameters and the properties of the self-excited pulsations.
Methods.
Output from global ‘star-in-a-box’ models computed with the
CO5BOLD
radiation-hydrodynamics code were analysed, particularly in regards to the pulsation properties, to find possible correlations with input and emergent stellar parameters. The fast Fourier transform was applied to spherically averaged mass flows to identify possible radial pulsation periods beneath the photosphere of the modelled stars. Stellar parameters were investigated for correlations with the extracted pulsation periods.
Results.
We find that the pulsation periods varied with the stellar parameters in good agreement with the current expectations. The pulsation periods follow Ritter’s period-mean density relation well and our AGB models agree with period-luminosity relations derived from observations. A mass estimate formula was derived from the 3D models, relating the stellar mass to the fundamental mode pulsation period and the stellar radius.
Conclusions.
While the non-linearity of the interplay between the self-excited pulsations and the self-consistent convection complicates analyses, the resulting correlations are in good agreement with respect to current theoretical and observational understandings.
Context . Knowing how the mass loss of carbon-rich AGB stars depends on stellar parameters is crucial for stellar evolution modelling, as well as for the understanding of when and how circumstellar ...structures emerge around these stars, e.g., dust shells and so-called detached shells of expelled gas.
Aims . The purpose of this paper is to explore the stellar parameter space using a numerical radiation hydrodynamic (RHD) model of carbon-star atmospheres, including a detailed description of dust formation and frequency-dependent radiative transfer, in order to determine how the mass loss of carbon stars changes with stellar parameters.
Methods . We have computed a grid of 900 numeric dynamic model atmospheres (DMAs) using a well-tested computer code. This grid of models covers most of the expected combinations of stellar parameters, which are the stellar temperature, the stellar luminosity, the stellar mass, the abundance of condensible carbon, and the velocity amplitude of the pulsation.
Results . The resultant mass-loss rates and wind speeds are clearly affected by the choice of stellar temperature, mass, luminosity and the abundance of available carbon. In certain parts of the parameter space there is also an inevitable mass-loss threshold, below which a dust-driven wind is not possible. Contrary to some previous studies, we find a strong dependence on the abundance of free carbon, which turns out to be a critical parameter. Furthermore, we have found that the dust grains that form in the atmosphere may grow too large for the commonly-used small-particle approximation of the dust opacity to be strictly valid. This may have some bearing on the wind properties, although further study of this problem is needed before quantitative conclusions can be drawn.
Conclusions . The wind properties show relatively simple dependences on stellar parameters above the mass-loss threshold, while the threshold itself is of a more complicated nature. Hence, we chose not to derive any simplistic mass-loss formula, but rather provide a mass-loss prescription in the form of aeasy-to-use FORTRAN routine. Since this mass-loss routine is based on data coming from an essentially self-consistent model of mass loss, it may therefore serve as a better mass-loss prescription for stellar evolution calculations than empirical formulae. Furthermore, we conclude that there are still some issues that need to be investigated, such as the role of grain-sizes.
Context.
The winds observed around asymptotic giant branch (AGB) stars are generally attributed to radiation pressure on dust formed in the extended dynamical atmospheres of these long-period ...variables. The composition of wind-driving grains is affected by a feedback between their optical properties and the resulting heating due to stellar radiation.
Aims.
We explore the gradual Fe enrichment of wind-driving silicate grains in M-type AGB stars to derive typical values for Fe/Mg and to test the effects on wind properties and synthetic spectra.
Methods.
We present new radiation-hydrodynamical DARWIN models that allow for the growth of silicate grains with a variable Fe/Mg ratio and predict mass-loss rates, wind velocities, and grain properties. Synthetic spectra and other observables are computed a posteriori with the COMA code.
Results.
The self-regulating feedback between grain composition and radiative heating, in combination with quickly falling densities in the stellar wind, leads to low values of Fe/Mg, typically a few percent. Nevertheless, the new models show distinct silicate features around 10 and 18 microns. Fe enrichment affects visual and near-IR photometry moderately, and the new DARWIN models agree well with observations in (
J
−
K
) versus (
V
−
K
) and
Spitzer
color–color diagrams. The enrichment of the silicate dust with Fe is a secondary process, taking place in the stellar wind on the surface of large Fe-free grains that have initiated the outflow. Therefore, the mass-loss rates are basically unaffected, while the wind velocities tend to be slightly higher than in corresponding models with Fe-free silicate dust.
Conclusions.
The gradual Fe enrichment of silicate grains in the inner wind region should produce signatures observable in mid-IR spectro-interferometrical measurements. Mass-loss rates derived from existing DARWIN models, based on Fe-free silicates, can be applied to stellar evolution models since the mass-loss rates are not significantly affected by the inclusion of Fe in the silicate grains.
Context.
The stellar winds of asymptotic giant branch (AGB) stars are commonly attributed to radiation pressure on dust grains, formed in the wake of shock waves that arise in the stellar ...atmospheres. The mass loss due to these outflows is substantial, and modelling the dynamical properties of the winds is essential both for studies of individual stars and for understanding the evolution of stellar populations with low to intermediate mass.
Aims.
The purpose of this work is to present an extensive grid of dynamical atmosphere and wind models for M-type AGB stars, covering a wide range of relevant stellar parameters.
Methods.
We used the DARWIN code, which includes frequency-dependent radiation-hydrodynamics and a time-dependent description of dust condensation and evaporation, to simulate the dynamical atmosphere. The wind-driving mechanism is photon scattering on submicron-sized Mg
2
SiO
4
grains. The grid consists of ~4000 models, with luminosities from
L
⋆
= 890
L
⊙
to
L
⋆
= 40 000
L
⊙
and effective temperatures from 2200 to 3400 K. For the first time different current stellar masses are explored with M-type DARWIN models, ranging from 0.75
M
⊙
to 3
M
⊙
. The modelling results are radial atmospheric structures, dynamical properties such as mass-loss rates and wind velocities, and dust properties (e.g. grain sizes, dust-to-gas ratios, and degree of condensed Si).
Results.
We find that the mass-loss rates of the models correlate strongly with luminosity. They also correlate with the ratio
L
*
∕
M
*
: increasing
L
*
∕
M
*
by an order of magnitude increases the mass-loss rates by about three orders of magnitude, which may naturally create a superwind regime in evolution models. There is, however, no discernible trend of mass-loss rate with effective temperature, in contrast to what is found for C-type AGB stars. We also find that the mass-loss rates level off at luminosities higher than ~14 000
L
⊙
, and consequently at pulsation periods longer than ~800 days. The final grain radii range from 0.25 to 0.6
μ
m. The amount of condensed Si is typically between 10 and 40%, with gas-to-dust mass ratios between 500 and 4000.
Abstract
Evolved low- and intermediate-mass stars that have reached the Asymptotic Giant Branch (AGB) phase tend to show pronounced long-period variability due to large-amplitude pulsations. Those ...pulsations are considered to play a key role in triggering mass loss through massive dusty winds. The winds enrich the surrounding interstellar medium with newly-produced chemical elements and dust grains, providing building blocks for new generations of stars and planets. Considerable efforts are being made to understand the physics of AGB stars, and to develop quantitative models. This talk gave a brief summary of recent developments, with references to the literature.
Context. Winds of asymptotic giant branch (AGB) stars are commonly assumed to be driven by radiative acceleration of dust grains. For M-type AGB stars, the nature of the wind-driving dust species has ...been a matter of intense debate. A proposed source of the radiation pressure triggering the outflows is photon scattering on Fe-free silicate grains. This wind-driving mechanism requires grain radii of about 0.1–1 micron in order to make the dust particles efficient at scattering radiation around the stellar flux maximum. Grain size is therefore an important parameter for understanding the physics behind the winds of M-type AGB stars. Aims. We seek to investigate the diagnostic potential of scattered polarized light for determining dust grain sizes. Methods. We have developed a new tool for computing synthetic images of scattered light in dust and gas shells around AGB stars, which can be applied to detailed models of dynamical atmospheres and dust-driven winds. Results. We present maps of polarized light using dynamical models computed with the DARWIN code. The synthetic images clearly show that the intensity of the polarized light, the position of the inner edge of the dust shell, and the size of the dust grains near the inner edge are all changing with the luminosity phase. Non-spherical structures in the dust shells can also have an impact on the polarized light. We simulate this effect by combining different pulsation phases into a single 3D structure before computing synthetic images. An asymmetry of the circumstellar envelope can create a net polarization, which can be used as diagnostics for the grain size. The ratio between the size of the scattering particles and the observed wavelength determines at what wavelengths net polarization switches direction. If observed, this can be used to constrain average particle sizes.
Context: The heavy mass loss observed in evolved asymptotic giant branch stars is usually attributed to a two-step process: atmospheric levitation by pulsation-induced shock waves, followed by ...radiative acceleration of newly formed dust grains. Detailed wind models suggest that the outflows of M-type AGB stars may be triggered by photon scattering on Fe-free silicates with grain sizes of about 0.1-1 mu m. As a consequence of the low grain temperature, these Fe-free silicates can condense close to the star, but they do not produce the characteristic mid-IR features that are often observed in M-type AGB stars. However, it is probable that the silicate grains are gradually enriched with Fe as they move away from the star, to a degree where the grain temperature stays below the sublimation temperature, but is high enough to produce emission features.
Aims: We investigate whether differences in grain temperature in the inner wind region, which are related to changes in the grain composition, can be detected with current interferometric techniques, in order to put constraints on the wind mechanism.
Methods: We use phase-dependent radial structures of the atmosphere and wind of an M-type AGB star, produced with the 1D radiation-hydrodynamical code DARWIN, to investigate if current interferometric techniques can differentiate between the temperature structures that give rise to the same overall spectral energy distribution.
Results: The spectral energy distribution is found to be a poor indicator of different temperature profiles and therefore is not a good tool for distinguishing different scenarios of changing grain composition. However, spatially resolved interferometric observations have promising potential. They show signatures even for Fe-free silicates (found at 2-3 stellar radii), in contrast to the spectral energy distribution. Observations with baselines that probe spatial scales of about 4 stellar radii and beyond are suitable for tracing changes in grain composition, since this is where effects of Fe enrichment should be found.
PDF
